Details

Time bar (total: 41.7s)

sample157.0ms

Algorithm
intervals
Results
49.0ms300×body80nan
36.0ms152×body160valid
27.0ms556×pre80true
17.0ms46×body320valid
7.0ms58×body80valid

simplify194.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
193.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune418.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.3b

localize22.0ms

Local error

Found 4 expressions with local error:

38.8b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.2b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.2b
(- (* b b) (* (* c a) 4))
0.1b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* difference-of-squares
5×pow1
4×flip3-- insert-posit16 flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp cbrt-unprod div-inv
Counts
4 → 76
Calls
4 calls:
Slowest
91.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
31.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
8.0ms
(- (* b b) (* (* c a) 4))
7.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series368.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
127.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
100.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
93.0ms
(sqrt (- (* b b) (* (* c a) 4)))
47.0ms
(- (* b b) (* (* c a) 4))

simplify5.7s

Counts
49 → 88
Calls
49 calls:
Slowest
608.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
419.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
364.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
330.0ms
(/ (* (* (- (sqrt (- (* b b) (* (* c a) 4))) b) (- (sqrt (- (* b b) (* (* c a) 4))) b)) (- (sqrt (- (* b b) (* (* c a) 4))) b)) (* (* (* 2 a) (* 2 a)) (* 2 a)))
218.0ms
(- b (* 2 (/ (* a c) b)))

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.4b

localize10.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0
Calls
0 calls:
Slowest

series0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

simplify0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

prune60.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.4b

localize25.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (* -2 (/ (* a c) b)) (* 2 a))
0.2b
(/ (* a c) b)

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
39×add-cbrt-cube add-exp-log
14×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
4×add-sqr-sqrt associate-/r* *-un-lft-identity times-frac add-cube-cbrt
2×pow1 clear-num frac-2neg insert-posit16 div-inv associate-/l* add-log-exp
1×associate-*r/ associate-/l/
Counts
2 → 53
Calls
2 calls:
Slowest
32.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
19.0ms
(/ (* a c) b)

series55.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
29.0ms
(/ (* a c) b)
26.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))

simplify11.4s

Counts
37 → 59
Calls
37 calls:
Slowest
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.2s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
894.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune538.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 5.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))
0.3b
(/ (* -2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) (* 2 a))
0.2b
(/ (* a c) b)
0.2b
(/ (* a c) b)

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
37×add-cbrt-cube add-exp-log
34×sqrt-prod
32×add-sqr-sqrt
20×*-un-lft-identity add-cube-cbrt
19×pow1 times-frac
12×swap-sqr prod-exp cbrt-unprod
10×cbrt-undiv div-exp associate-*r* associate-*l*
8×sqrt-pow1 pow1/2 sqrt-div
7×associate-/r* div-inv
5×associate-*r/ pow-prod-up
4×insert-posit16 add-log-exp unswap-sqr
3×clear-num frac-2neg pow-prod-down pow-sqr associate-/l* associate-/l/
2×frac-times associate-*l/
1×pow2 rem-square-sqrt pow-plus sqrt-unprod *-commutative
Counts
4 → 138
Calls
4 calls:
Slowest
120.0ms
(/ (* -2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) (* 2 a))
50.0ms
(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))
14.0ms
(/ (* a c) b)
8.0ms
(/ (* a c) b)

series213.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
89.0ms
(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))
49.0ms
(/ (* -2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) (* 2 a))
39.0ms
(/ (* a c) b)
36.0ms
(/ (* a c) b)

simplify13.5s

Counts
133 → 150
Calls
133 calls:
Slowest
1.6s
(/ (* (* (* -2 -2) -2) (* (* (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))) (sqrt (/ (* a c) b))) (* (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))) (sqrt (/ (* a c) b))))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.3s
(/ (* (* (* -2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) (* -2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))))) (* -2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.3s
(/ (* (* (* -2 -2) -2) (* (* (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))) (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.0s
(/ (* (* (* -2 -2) -2) (* (* (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))) (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))))) (* (* (* 2 2) 2) (* (* a a) a)))
987.0ms
(/ (* (* (* -2 -2) -2) (* (* (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))) (sqrt (/ (* a c) b))) (* (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))) (sqrt (/ (* a c) b))))) (* (* (* 2 2) 2) (* (* a a) a)))

prune1.5s

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 5.3b

regimes524.0ms

Accuracy

10.6% (6.2b remaining)

Error of 11.3b against oracle of 5.1b and baseline of 12.0b

bsearch65.0ms

end0.0ms

sample5.6s

Algorithm
intervals
Results
1.4s16347×pre80true
1.4s4789×body160valid
1.3s8347×body80nan
684.0ms1393×body320valid
295.0ms1818×body80valid